The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A115135 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A115135

Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+617)^2 = y^2.
(history; published version)

#15 by Charles R Greathouse IV at Thu Sep 08 08:45:23 EDT 2022

PROG

(MAGMAMagma) I:=[0, 108, 1407, 1851, 2407, 9768, 12340]; [n le 7 select I[n] else Self(n-1) +6*Self(n-3) -6*Self(n-4) -Self(n-6) +self(n-7): n in [1..30]]; // G. C. Greubel, May 04 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#14 by N. J. A. Sloane at Sat Feb 15 10:52:26 EST 2020

AUTHOR

_Mohamed Bouhamida (bhmd95(AT)yahoo.fr), _, Jun 03 2007

Discussion

Sat Feb 15

10:52

OEIS Server: https://oeis.org/edit/global/2849

#13 by Alois P. Heinz at Fri May 04 18:07:09 EDT 2018

STATUS

proposed

approved

#12 by G. C. Greubel at Fri May 04 16:43:42 EDT 2018

STATUS

editing

proposed

#11 by G. C. Greubel at Fri May 04 16:43:34 EDT 2018

LINKS

G. C. Greubel, <a href="/A115135/b115135.txt">Table of n, a(n) for n = 1..1000</a>

FORMULA

a(n) = 6*a(n-3) -a(n-6) +1234 for n > 6; a(1)=0, a(2)=108, a(3)=1407, a(4)=1851, a(5)=2407, a(6)=9768.

G.f.: x*(108 +1299*x +444*x^2 -92*x^3 -433*x^4 -92*x^5) / ((1-x)*(1 -6*x^3 +x^6)).

MATHEMATICA

LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {0, 108, 1407, 1851, 2407, 9768, 12340}, 50] (* G. C. Greubel, May 04 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(x*(108 +1299*x +444*x^2 -92*x^3 -433*x^4 -92*x^5)/((1-x)*(1 -6*x^3 +x^6))) \\ G. C. Greubel, May 04 2018

(MAGMA) I:=[0, 108, 1407, 1851, 2407, 9768, 12340]; [n le 7 select I[n] else Self(n-1) +6*Self(n-3) -6*Self(n-4) -Self(n-6) +self(n-7): n in [1..30]]; // G. C. Greubel, May 04 2018

STATUS

approved

editing

#10 by Charles R Greathouse IV at Sun Jun 18 02:25:44 EDT 2017

LINKS

<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).

Discussion

Sun Jun 18

02:25

OEIS Server: https://oeis.org/edit/global/2678

#9 by Charles R Greathouse IV at Sat Jun 13 00:52:02 EDT 2015

LINKS

<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).

Discussion

Sat Jun 13

00:52

OEIS Server: https://oeis.org/edit/global/2439

#8 by Charles R Greathouse IV at Fri Jun 12 15:26:00 EDT 2015

LINKS

<a href="/index/Rea#recLCCRec">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).

Discussion

Fri Jun 12

15:26

OEIS Server: https://oeis.org/edit/global/2436

#7 by Russ Cox at Fri Mar 30 17:27:48 EDT 2012

EXTENSIONS

Edited and two terms added by _Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, May 18 2009

Discussion

Fri Mar 30

17:27

OEIS Server: https://oeis.org/edit/global/145

#6 by Charles R Greathouse IV at Wed Dec 28 10:25:39 EST 2011

STATUS

editing

approved